In this paper, we propose a nonlocal Weickert type PDE for the multiframe super-resolution task. The proposed PDE can not only preserve singularities and edges while smoothing, but also can keep safe the texture much better. This PDE is based on the nonlocal setting of the anisotropic diffusion behavior by constructing a nonlocal term of Weickert type, which is known by its coherence enhancing diffusion tensor properties. A mathematical study concerning the well-posedness of the nonlocal PDE is also investigated with an appropriate choice of the functional space. This PDE has demonstrated its efficiency by combining the diffusion process of Perona-Malik in the flat regions and the anisotropic diffusion of the Weickert model near strong edges, as well as the ability of the non-local term to preserve the texture. The elaborated experimental results give a great insight into the effectiveness of the proposed nonlocal PDE compared to some PDEs, visually and quantitatively.

中文翻译：

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一种应用于多帧超分辨率的非局部 Weickert 型偏微分方程

在本文中，我们为多帧超分辨率任务提出了一种非局部 Weickert 型 PDE。所提出的 PDE 不仅可以在平滑的同时保留奇异点和边缘，而且可以更好地保持纹理的安全。通过构造Weickert类型的非局部项，该PDE基于各向异性扩散行为的非局部设置，该项以其相干性增强了扩散张量特性而闻名。还通过适当的功能空间研究了关于非局部PDE良好姿势的数学研究。该 PDE 通过将平坦区域中 Perona-Malik 的扩散过程和强边缘附近的 Weickert 模型的各向异性扩散以及非局部项保留纹理的能力相结合，证明了其效率。